How can Siamese Networks be viewed as RNNs?
Well, here in the picture we have the unrolled or unfold RNN on the right side. Siamese network is formed when it is said to be "unrolled over two time-steps". So, take part where there is two first iterations of RNN and yes, you have kind of Siamese network.

One take from the source of the image:


  Unlike a traditional deep neural network, which uses different parameters at each layer, a RNN shares the same parameters (U, V, W above) across all steps. This reflects the fact that we are performing the same task at each step, just with different inputs. This greatly reduces the total number of parameters we need to learn.


Sounds familiar to siamese network used on single-object tracking: there we take two signals (image and the tracked object), drive it through identical paths and make some maths to get results. Just something the RNN makes to time separated values!

For proof of similarity, a take from a site where siamese networks are nicely explained:



Side note: I don't know then, how closely those relate in real world (could a Siamese network in anyway be a RNN or vice versa), but supposedly so, because the comparison is made by researcher to say so. At diagrammatic level at least there would be no problem on that.